Multi-input multi-output automatic design synthesis for performance and robustness

Abstract

A direct-design method for solving the problem of robustness to cross-coupling perturbations in multivariable control systems is presented. The method uses numerical optimization procedures to manipulate the system feedback gains as direct design variables. The manipulation is accomplished in a manner that produces desired performance by pole placement and robustness by modification of the minimum singular values of the system return difference matrix. Channels affected by cross-coupling perturbation may be recognized by the character of their transfer function plots. The mechanism used by the pole placement and robustness routine in obtaining a robust design is evident from the gain changes associated with the Bode diagrams and the zero shifts shown on pole-zero plots. The pole placement and robustness routine uses gain equalization and zero assignment to modify the characteristics of the system in the design. A modification of the pole placement and robustness routine that may be applied to the design of robust observers is also presented. Using feedback and filter gains as direct design variables, a practical design procedure for robustness recovery in observer-based systems is obtained.